Method for Associating a Digital Image with a Class of a Classification System

ABSTRACT

Disclosed is a method for assigning the content of a digital image to a class of a classification system. Said method comprises the following steps: —a predetermined number of F numerical shape characteristics ψ m  are determined; —the value of each shape characteristic of the F numerical shape characteristics determined for the image is compared to the value filed in a table for the respective shape characteristic, values for the individual numerical shape characteristics being allocated to each class in the table; —the class in which the F numerical shape characteristics determined for said image correspond best to the values of the numerical shape characteristics indicated in the table for said class is output as the class into which the image that is to be recognized is classified.

The invention relates to a method for associating a digital image with aclass of a classification system.

Automating error recognition based on optical analysis methods hasbecome increasingly important with the increasing automation ofindustrial processes. Optical error recognition methods were performedin the past by quality assurance personnel, who inspected the object tobe tested or an image representation of the object to be tested andidentified possible errors. For example, x-ray images of weld seams arechecked based on error types, such as for example tears, inadequatecontinuous welds, adhesion errors, slag, slag lines, pores, tubularpores, root notches, root errors, heavy-metal inclusions and edgeoffset. It is also known to inspect radioscopic images of cast parts toidentify errors in the cast part, for example inclusion of impurities,inclusion of gases, bubbles, such as axial pores or spongy pores,fissures or chaplets. Because of these errors are of similar type, butmay be different in their appearance and shape, more recent approachesin industrial error evaluation now associate errors with differentclasses, wherein the respective class contains errors of the same type.The industry standard EN 1435 describes, for example, the classificationsystem for weld seam errors. According to this standard, the errorsoccurring in weld seams and identified by x-ray images are divided intothe 30 different classes, for example classes for the error tear, suchas longitudinal care or transverse tear, inadequate continuous welds,adhesion errors, foreign inclusions, such as slag, slag lines, gasinclusions, such as pores or tubular pores, or heavy-metal inclusions,undercuts, root notches, root errors, and edge offset. With increasingautomation of these processes, there is now a push to achieve opticalrecognition of errors and association of these errors with predeterminedclasses through image analysis based on images that are recorded andstored using digital image recording techniques. Conventional automatederror recognition methods based on digital images use a so-called“heuristic approach.” With this approach, reference images are saved inan image processing unit and an attempt is made to through imagecomparison to associate the content of a digital image with one of thesereference patterns.

In other technical fields, image content is associated with classes of aclassification system, for example, for character recognition. In thiscase, for example, each letter forms its own class, so that for thecapital letter alphabet there exist, for example, 26 classes, namely forthe characters (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, Z). The OCR technologies (Optical CharacterRecognition) analyze the digital image of a printed page generated by ascanner and associate the individual letter symbols with thepredetermined classes. As a result, the OCR technology “recognizes” thetext and can transfer the classified characters to a text processingprogram as an editable sequence of letters. The granted European patents0 854 435 B1 and 0 649 113 B1 are directed, for example, to thetechnical field of character recognition (Optical CharacterRecognition).

The technique of image processing can be more and more divided intoareas with different sub-processes, whose technologies developindependent of each other. These areas are frequently organized intoimage preprocessing, image analysis, analysis of image sequences, imagearchiving and the so-called Imaging.

Image preprocessing is defined as the computer-aided improvement of thequality (processing: noise elimination, smoothing) of the correspondingdigital image to facilitate visual recognition of the informationcontent of this image by the viewer.

Image analysis is defined as the computer-aided evaluation of theinformation content of the corresponding digital image by automated andreproducible structuring, identification and comprehension of thisimage.

Analysis of image sequences is defined as the computer-aided evaluationof the information content of the respective sequence of digital imagesby automated and reproducible structuring, identification andcomprehension of all individual images of this sequence and by automatedand reproducible comprehension of the context of the sequence ofindividual images of this image sequence.

Image archiving is defined as the computer-aided compression and storageof the digital images together with indexed search descriptors from acontrolled vocabulary.

Imaging is defined as the computer-aided generation of syntheticgraphics and digital images for visualizing and describing theinformation content of complex processes on an image and symbol planefor the human observer.

The technique of associating the content of digital images with a classof the classification system is one method of image analysis, which canbe divided into three subareas: segmentation, object recognition andimage comprehension.

Segmentation is defined as of the automated and reproducible structuringof the respective digital images by separating the objects that arerelevant for the analysis of the image from each other and from theimage background. Object recognition is defined as the automated andreproducible classification of the separated objects. Imagecomprehension can be interpreted as the automated and reproducibleinterpretation of the respective digital image by context evaluation ofthe classified, separated objects. The technique of associating digitalimages with a class of a classification system is a method of objectrecognition.

Object recognition can be viewed as a subarea of pattern recognition,namely as the subarea of the pattern recognition which recognizes aspatterns only two-dimensional objects in images.

Images are typically displayed as an image composed of pixels, wherebyto display the image, the content of each pixel and its position in theimage must be known. Depending on the content attribute, the image iscan be divided into color images, grayscale images and binary images,wherein binary images have as content attribute, for example, only thevalues 0 and 1 for black and white, respectively.

One method frequently used in this technology for associating a digitalimage with a class of a classification system, which was usedsuccessfully for decades for distinguishing military aircraft(friend-foe identification), is known from M. K. Hu: “Visual PatternRecognition by Moment Invariants”, IRE Trans. Info. Theory, vol. IT-8,1962, pp. 179-187 and R. C. Gonzalez, R. E. Woods: “Digital ImageProcessing”, Addison-Wesley Publishing Company, 1992, pp. 514-518. Basedon the so-called normalized centralized axial moments obtained throughimage analysis techniques from the image display, a finite sequence {φ₁}of 7 dimensionless shape attributes can be generated for an arbitrary,separated, in limited, two-dimensional object in a binary image byscaling. If the 7 sequential elements Φ_(I) (0≦I≦I₀=7) are viewed as thecoordinates of an attribute vector Φ=(Φ₁, Φ₂, Φ₃, Φ₄, Φ₅, Φ₆, Φ₇) whichis an element of a 7-dimensional Euclidian attribute space M₇, then thismethod induces an object recognition in this 7-dimensional attributespace M₇. The method has the advantage, compared with object recognitionby heuristic attributes, that classification occurs exclusively withattribute vectors Φ=(Φ₁, Φ₂, Φ₃, Φ₄, Φ₅, Φ₆, Φ₇) whose coordinates aredimensionless shape attributes, so that in particular size differencesbetween the objects to be recognized and the objects used for generatingthe comparison table become unimportant. In addition, a uniquesequential order with respect to the relevance of the attributes for theobject recognition and the digital image processing is defined withinthe set of the dimensionless shape attributes φ₁ through the coordinatereference to the attribute vector Φ so that it is immediately clear thatthe first attribute Φ₁ is the most important.

However, this method still has disadvantages because the number of theavailable dimensionless shape attributes is limited to 7 and amisclassification can therefore occur with complex objects, if twodifferent classes have identical values for the 7 dimensionless shapeattributes.

In view of this background information, it is an object of the inventionto propose a method for associating the content of a digital image witha class of a classification system which makes it possible to reliablyrecognize also symbols having a more complex shape.

This object is solved with the method according to claim 1. Advantageousembodiments are recited in the dependent claims.

The invention is based on the concept of determining for the image to beanalyzed a predetermined number of numerical shape attributes ψ_(m)wherein m is a running index having values from 1 to F, wherein ψ_(m) isa transformed expression of the dimensionless, scaled, normalized,centralized, polar moment ρ^(m) . For associating the content of thedigital image, these mutually independent shape attributes ψ_(m) can becompared with values for these shape attributes saved in a table. If thevalues of all determined F shape attributes ψ_(m) are identical to the Fshape attributes ψ_(m) saved in the table, then the image content of theanalyzed image belongs to this class. Because of the digitization, it ispreferable to work with approximate values, so that a class associationis already displayed when the computed F shape attributes ψ_(m) agreeapproximately with the saved F shape attributes ψ_(m).

Unlike the conventional method which is limited to 7 shape attributes,the numerical shape attributes ψ_(m) proposed for image analysis in thepresent invention are independent of each other in such a way that alarge number of shape attributes can be defined, without creating aninterdependence of the shape attributes. In this way, an unambiguousassociation of the image contents to be recognized with a predeterminedclass can be achieved.

In particular, the method of the invention is independent of therelative position of the content to be recognized with respect to theacquisition device. Even objects rotated by, for example, 60° or 180°can be uniquely associated.

The method is based on computing is sequence of F functionallyindependent, dimensionless attributes of the separated, limited contentin the presented image.

The image is conventionally represented by N pixels, wherein a pixel ina predetermined coordinate system is located at the position (x_(i),y_(i)) and the image extends from the coordinates (0, 0) to (x_(imax),y_(jmax)) and imax is the maximum number of pixels in the direction ofthe x-coordinate and ymax is the maximum number of pixels in thedirection of the y-coordinate, and wherein a content attribute data [j,i] is associated with each pixel.

The content attribute for a binary image, where the corresponding imagepixel content assumes, for example, the value 1 or 0 for black or white,is for example a single value saved in a table, and data [j,i] isrepresentative for the value in this table at the position associatedwith the pixel. In color images, where the content attribute of eachpixel is composed, for example, of three values for the 3 colorrepresentation “red, green, blue” (RGB representation), the contentattribute data [j,i] is, for example, representative of a vector whichhas these three values for the respective pixel. Data [j,i] can also berepresentative of other vectors, if other color representations areused, e.g., grayscale representations. Data [j,i] can also berepresentative of the magnitude of such vector, when a multi-colorrepresentation is converted from a multi-color representation, forexample an RGB representation, into a grayscale or even a binaryrepresentation before employing the classification method of theinvention.

In a color representation, for example an RGB representation, data [j,i]can also represent the individual value of the red representation, orthe green representation, or the blue representation in the pixel. Theclassification method is then performed, for example, exclusively basedon one representation, for example the red representation, whereby themethod is here performed identical to the preceding method for binaryrepresentations. In this case, binary values 1 and 0 can also be usedfor data [j,i] at the pixel, wherein for example 1 indicates red and 0empty. The classification method can also be performed in parallel forthe different color representations, i.e., in parallel for a binary redrepresentation, a binary green representation and a binary bluerepresentation. This increases the accuracy of the classification.

The moment ρ^(m) transformed into the numerical shape attribute ψ_(m) iscomputed from

$\overset{\_}{\rho^{m}} = {k_{m}\overset{\_}{R^{m}}}$${{with}\mspace{14mu} k_{m}} = {\frac{\left( {m + 2} \right)}{2}\left( \frac{\pi}{A} \right)^{\frac{m}{2}}}$$A = {m_{0,0} = {{\Delta \; a} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{{data}\left\lbrack {j,i} \right\rbrack}}}}}$$\overset{\_}{R^{m}} = {\frac{\upsilon_{m}}{\upsilon_{0}} = \frac{\upsilon_{m}}{m_{0,0}}}$$\upsilon_{m} = {{\Delta \; a} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {R\left( {j,i} \right)} \right)^{m}{{data}\left\lbrack {j,i} \right\rbrack}}}}}$${R\left( {j,i} \right)} = \sqrt{\left( {{\left( {{i - 0},5} \right) \star {\Delta \; a}} - \overset{\_}{x}} \right)^{2} + \left( {{\left( {{j = 0},5} \right) \star {\Delta \; b}} - \overset{\_}{y}} \right)^{2}}$$\overset{\_}{x} = \frac{m_{1,0}}{m_{0,0}}$$\overset{\_}{y} = \frac{m_{0,1}}{m_{0,0}}$$m_{1,0} = {\left( {\Delta \; a} \right)^{2} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {{i - 0},5} \right) \star {{data}\left\lbrack {j,i} \right\rbrack}}}}}$$m_{0,1} = {\left( {\Delta \; b} \right)^{2} \star {\Delta \; a} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {{j - 0},5} \right) \star {{data}\left\lbrack {j,i} \right\rbrack}}}}}$

Δa=width of the pixel in the x-coordinate direction,Δb=width of the pixel in the y-coordinate direction,data [j, i]=content attribute of the pixel at the position (y_(j),x_(i))m=a sequential number from 1 to F.

In a particularly preferred embodiment, the predetermined coordinatesystem is a Cartesian coordinate system, because the majority of digitalimages defines the pixels with reference to a Cartesian coordinatesystem. However, other coordinate systems, for example polar coordinatessystems, can also be employed.

While presently digital images can be rendered typically with between 1and 3 million image dots (pixels), it can be expected that the number Nwill increase with advances of image acquisition and image processingtechniques, so that the afore-described sum functions will approachintegral functions.

More particularly, an image content is defined by the arrangement ofpixels having the same content attribute.

The F determined shape attributes of the image content define anattribute vector in a limited, F-dimensional attribute space (unithypercube). The content classification occurs by problem-specificclustering of this n-dimensional.

The classification system can be, for example, a predetermined industrystandard, for example EN 1435. For identification of persons, forexample, each person can form an individual class. In this case, the Fshape attributes ψ_(m) representative of the fingerprint or the irisimage of the person to be identified are then saved in the comparisontable. For identification of persons, the image of the iris acquired bythe image acquisition unit, for example a camera, is analyzed with themethod of the invention, whereby the F shape attributes ψ_(m) of therecorded iris are computed and compared with the shape attribute valuessaved in the table. If there is an (approximate) agreement with allvalues of the shape attributes ψ_(m) of a class, then the system hasrecognized the person characterized by this class. Preferably, aleast-squares method, for example a method according to Gauss, can beused to establish the approximate agreement.

If a digital image is recognized that is represented in a representationdifferent from a binary representation, then the aforementioned methodsteps can be performed for several groups with F numerical shapeattributes ψ_(m), for example, for one group for values of a redrepresentation, for one group for values of a green representation, andfor one group for values of a blue representation. Alternatively, theaforementioned method steps can also be performed on content attributesdata [j,i] which contain the individual values of the individual colorrepresentations as a vector. Computational division operations are thenpreferably performed on the magnitudes of the vectors.

In a preferred embodiment, the shape attribute ψ_(m) is determined bythe transformation

$\psi_{m} = {\sqrt[m]{\frac{1}{\overset{\_}{\rho^{m}}}}.}$

However, other transformations as can also be used to transform ψ_(m) toρ_(m) , and ψ_(m) may even be ρ^(m) .

The shape attribute to be compared with the values stored in the tableis preferably the shape attribute ψ_(m) obtained with the aforementionedtransformation. Before the comparison with the table values or in thetransformation from ρ^(m) , the sequential order of the F shapeattributes can be subjected to an orthogonalization method, for exampleas performed in E. Schmidt. In this approach, the shape attributes to becompared can be recomputed so as to yield for a circle a sequence of Fshape attributes ψ₁, ψ₂, ψ₃, ψ₄, ψ₅ . . . ψ_(F) with values of 1, 0, 0,0, 0 . . . 0.

For defining the number F of the numerical shape attributes ψ_(m), thenumber F can be increased, starting with F=1, from several, inparticular more than 29 samples per class of the classification system,until the values for the respective shape attribute ψ_(m) determined forthe samples of a class are different in at least one numerical value forat least one shape attribute ψ_(m) from the numerical value of thisshape attribute ψ_(m) of the other class. In a particularly preferredembodiment, the number F of the shape attributes is increased until thevalues of the shape attributes with the highest ordinal numbers m in allclasses decrease with increasing ordinal number. The values of thecorresponding shape attribute ψ_(m) determined for the at least 29samples per class can be arithmetically averaged in order to determine avalue to be inserted for this class for this shape attribute.

The table reproduced below, which is intended only to illustrate thefreely selected numerical values, shows that for determining the weldseam error in relation to the error classes “tear”, “pore”, “tubularpore”, a number F=1 of the numerical shape attributes ψ_(m) is notsufficiently precise, because ψ₁ assumes almost identical values for thetear class as for the tubular pore classes. The association only becomesunique by including the second numerical shape attribute ψ₂. As can beseen, in spite of the similar numerical values for ψ₂ in the class“pore” and “tubular pore”, this system consisting of only two shapeattributes ψ₁, ψ₂ is suitable to precisely classify the 3 errors.

Tear Pore Tubular pore ψ₁ 0.01245 0.87231 0.01268 ψ₂ 0.00234 0.541000.54612

The number F can also be determined by a method based on a rotationalellipse. Such “Cluster Methods” are described, for example, in H.Niemann, Klassifikation von Mustern (Pattern Classification), SpringerVerlag, Berlin, 1983, page 200ff.

The method of the invention for associating the content of a digitalimage with a class of a classification system is employed preferably inthe optical inspection of components, in particular in optical surfaceinspection. The method can also be used in quality assurance, texture,shape and contour analysis, photogrammetry, symbol and text recognition,personnel recognition, robotic vision or evaluation of radiographic orradioscopic images, ultrasound images and nuclear spin tomography.

It is thereby unimportant if the images having objects to be recognizedare “optical” images in the spectral range of visible light orradiographic or radioscopic images, or even synthetic images from thetechnical field Imaging. The method can therefore be used in the fieldof optical surface inspection as well as in quality assurance, texture,shape and contour analysis, photogrammetry, symbol and text recognition,personnel recognition, robotic vision or evaluation of radiographic orradioscopic images, ultrasound images and nuclear spin tomography.

When a concrete problem of object recognition is approached in thecontext of this broad range of possible applications, then the degree ofcomplexity of the problem is defined from the beginning:

It is known into how many different object classes K the objects to berecognized are to be sorted. Unlike with classification based onheuristic attributes, in the new algorithmic method the number ofdegrees of freedom of the shape can be experimentally determined withrespect to each object class based on a representative random samplingof test objects. The classification is performed exclusively withattribute vectors ψ=(ψ₁, ψ₂, ψ₃, ψ₄, ψ₅, . . . , ψ_(F)). The attributevector of an arbitrary separated, limited, two-dimensional object in theimage is located inside a limited, normalized F-dimensional subarea(“unit hypercube”) of an F-dimensional attribute space. The patternclassification is performed by a problem-specific clustering of theinterior of this F-dimensional unit hypercube.

The invention will now be described with reference to a drawingdepicting a single exemplary embodiment. It is shown in:

FIG. 1 three different representations of a first symbol to berecognized;

FIG. 2 three representations of a second symbol to be recognized; and

FIG. 3 three representations of a third symbol to be recognized.

FIGS. 1, 2 and 3 show the letters A, B, and C in three representationsi) normal, ii) normal, but rotated by 90°, iii) same orientation asnormal, but smaller. In addition to the central orientation depicted inthe Figures, positioning to the left and positioning to the right werealso investigated.

The following Table shows the values for ψ₁, wherein ψ₁ is computed fromthe relation

$\psi_{1} = {\sqrt[1]{\frac{1}{\overset{\_}{\rho^{1}}}}.}$

ρ¹ is obtained from the following relationships:

$\overset{\_}{\rho^{1}} = {k_{1}\overset{\_}{R^{1}}}$${{with}\mspace{14mu} k_{1}} = {\frac{3}{2}\left( \frac{\pi}{A} \right)^{\frac{1}{2}}}$

-   -   Δa=width of the pixel in the x-coordinate direction    -   =Δa=0,3175 mm    -   Δb=width of the pixel in the y-coordinate direction    -   =Δb=0,3175 mm    -   data [j,i]=content attribute of the pixel at the position        (y_(j), x_(i)).

With the afore-described relationship and the respective data fields forthe respective representations, where content attributes are saved atthe positions (y_(j), x_(i)), the values reproduced in the followingtable are obtained:

Letter Position Magnitude Orientation Attribute ψ₁ A left 96 normal0.576 A centered 96 normal 0.576 A right 96 normal 0.576 A left 96 90°rotated 0.574 A centered 96 90° rotated 0.574 A right 96 90° rotated0.574 A left 48 normal 0.569 A centered 48 normal 0.569 A right 48normal 0.569 B left 96 normal 0.609 B centered 96 normal 0.609 B right96 normal 0.609 B left 96 90° rotated 0.608 B centered 96 90° rotated0.608 B right 96 90° rotated 0.608 B left 48 normal 0.598 B centered 48normal 0.598 B right 48 normal 0.598 C left 96 normal 0.445 C centered96 normal 0.445 C right 96 normal 0.445 C left 96 90° rotated 0.444 Ccentered 96 90° rotated 0.444 C right 96 90° rotated 0.444 C left 48normal 0.443 C centered 48 normal 0.443 C right 48 normal 0.443

Table of the numerical values for the shape attribute ψ₁

As can be seen, the value ψ₁ for the letter A assumes values of about0.57, for the letter B values of about 0.6, and for the letter C valuesof about 0.44. A previously defined symbol can therefore be uniquelyrecognized with the method of the invention independent of the actualposition and size of the letter.

1. A method for associating the content of a digital image with a class of a classification system, wherein the image is represented by N pixels, a each pixel being located at the position (x_(i), y_(j)) in a predetermined coordinate system said image extending from the coordinates (0, 0) to (x_(imax), y_(jmax)) and imax being the maximum number of pixels in the direction of the x-coordinate and jmax is the maximum number of pixels in the direction of the y-coordinate and wherein at least one numerical content attribute data [j, i] is associated with each pixel, said method comprising the steps of: determining at least one group of a predetermined number of F numerical shape attributes ψ_(m) with m as a running index, wherein ψ_(m) is a transformed expression of the moment ρ^(m) , and ρ^(m) is derived from $\overset{\_}{\rho^{m}} = {k_{m}\overset{\_}{R^{m}}}$ ${{with}\mspace{14mu} k_{m}} = {\frac{\left( {m + 2} \right)}{2}\left( \frac{\pi}{A} \right)^{\frac{m}{2}}}$ $A = {m_{0,0} = {{\Delta \; a} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{{data}\left\lbrack {j,i} \right\rbrack}}}}}$ $\overset{\_}{R^{m}} = {\frac{\upsilon_{m}}{\upsilon_{0}} = \frac{\upsilon_{m}}{m_{0,0}}}$ $\upsilon_{m} = {{\Delta \; a} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {R\left( {j,i} \right)} \right)^{m}{{data}\left\lbrack {j,i} \right\rbrack}}}}}$ ${R\left( {j,i} \right)} = \sqrt{\left( {{\left( {{i - 0},5} \right) \star {\Delta \; a}} - \overset{\_}{x}} \right)^{2} + \left( {{\left( {{j = 0},5} \right) \star {\Delta \; b}} - \overset{\_}{y}} \right)^{2}}$ $\overset{\_}{x} = \frac{m_{1,0}}{m_{0,0}}$ $\overset{\_}{y} = \frac{m_{0,1}}{m_{0,0}}$ $m_{1,0} = {\left( {\Delta \; a} \right)^{2} \star {\Delta \; b} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {{i - 0},5} \right) \star {{data}\left\lbrack {j,i} \right\rbrack}}}}}$ $m_{0,1} = {\left( {\Delta \; b} \right)^{2} \star {\Delta \; a} \star {\sum\limits_{j = 1}^{j\mspace{11mu} \max}{\sum\limits_{i = 1}^{i\mspace{11mu} \max}{\left( {{j - 0},5} \right) \star {{data}\left\lbrack {j,i} \right\rbrack}}}}}$ wherein Δa=width of the pixel in the x-coordinate direction, Δb=width of the pixel in the y-coordinate direction, data [j, i]=content attribute of the pixel at the position (y_(j), x_(i)) m=a number running from 1 to F as a counter of the shape attributes; comparing the value of each shape attribute of the F numeric shape attributes intended for the picture in the at least one group with the value saved in a table for the respective shape attribute of this group, wherein values for the individual numerical shape attributes of this group in the table are associated with each class; and outputting the class as an association class in which the image to be recognized is classified, in which the F numeric shape attributes intended for the picture best correspond to the values of the numeric shape attributes recorded in the table for this class.
 2. The method of claim 1, wherein the shape attribute ψ_(m) is determined by the transformation $\psi_{m} = {\sqrt[m]{\frac{1}{\overset{\_}{\rho^{m}}}}.}$
 3. The method of claim 1, further comprising the step of determining the number F of the numeric shape attributes ψ_(m) from at least 29 samples per class of the classification system, wherein the number F is increased until the values for the shape attributes ψ_(m) obtained for the samples of one class are different for at least one shape attribute ψ_(m) from the numerical values of this shape attribute ψ_(m) of the other classes.
 4. The method of claim 1, further comprising the steps of associating errors of cast parts to error classes defined in an industrial standard, and generating the digital image by radioscopy.
 5. The method of claim 1, further comprising the steps of associating errors of weld seams to error classes defined in an industrial standard, and generating the digital image by radioscopy.
 6. The method of claim 1, further comprising the steps of associating objects reproduced on paper to classes defined for objects reproduced on paper, and generating the digital image with a scanner.
 7. The method of claim 6, wherein said classes are defined for objects that include elements of a text.
 8. The method of claim 6, wherein said classes are defined for objects that include elements of a musical score.
 9. The method of claim 1, wherein individual values of individual color representations are included in content attributes data [i, j] as a vector.
 10. The method of claim 1, further comprising the step of a parallel execution of said steps of determining, comparing and outputting for an image having more than a binary representation, so that each of said parallel executions provides a respective class for a respective representation of the image.
 11. The method of claim 1, further comprising the step of generating an optical image as the digital image.
 12. The method of claim 1, further comprising the step of generating an image of a person and a least squares method is used to determine whether the person has been recognized.
 13. The method of claim 12, wherein the image of a person is an image of a fingerprint.
 14. The method of claim 12, wherein the image of a person is an image of an iris.
 15. The method of claim 1, further comprising the step of repeating said steps of determining, comparing and outputting for an image having more than a binary representation, so that each repetition provides a respective class for a respective representation of the image.
 16. The method of claim 1, further comprising the step of determining the number F of the numeric shape attributes ψ_(m) using a rotational ellipse.
 17. The method of claim 1, further comprising the step of generating an optical image as the digital image.
 18. The method of claim 10, wherein the optical image is an optical image of the surface of a component.
 19. The method of claim 1, further comprising the step of generating a radioscopic image as the digital image.
 20. The method of claim 1, further comprising the step of generating an ultrasound image as the digital image.
 21. The method of claim 1, further comprising the step of generating a nuclear spin tomography image as the digital image.
 22. The method of claim 1, further comprising the step of generating a synthetic image as the digital image. 